Multi-scale Analysis And Structural Modeling Of Particle Pair Dynamics In Subgrid Scale

Particle-laden flow is a multi-scale problem and the complex interactions between particles and fluid is one of the main difficulties.In Large eddy simulation(LES),the influences of sub-grid scale(SGS)fluid motions on particle statistics cannot be ignored.Quantitative analysis of such influences and the construction of reasonable particle SGS velocity model are still one of the research hotspots in this field.In this paper,the gas-particle homogeneous isotropic turbulent(HIT)flow is taken as the research object,and the following research is carried out on the interaction of SGS motions and inertial particles:Firstly,the Fourier transform is used to perform the cut-off filtering of the direct numerical simulation(DNS)flow field in spectral space,and the filtered flow fields(FDNS)under different truncated wave numbers are obtained.Then the inertial particles are released in different fields and the Lagrangian point particle model is used for particle tracking.The focus is on the influence of the filtered SGS motions on the kinetic statistics of the particles,especially the radial distribution function(RDF)for which the error curve exhibits a nonmonotonic variation.For small inertial particles,the absence of SGS motions leads to a decrease in the RDF,but for particles with Stk > 3.0,it increases after filtering.On the whole,the scale shift occurs in the RDF curve is the key,and similar phenomenon is found in the high-order statistics of the radial relative velocity(RRV)of the particle-pairs and also the flow structures seen by the particles.This indicates that the increase in the characteristic scales of the flow field after filtering affects the particles interacting with it,and also it is verified that there is a strong correlation between the RDF and RRV,which is closely related to the SGS motions in the field.The particle collision kernel embodies the combined effect of the RDF and RRV.The results show that the influences of the SGS motions on the collision-related statistics is obvious only for Stk ? 2.0 under their complementary processes,so as to the modelling works.Secondly,the wavelet filter is used to extract the multi-scale coherent vortex structure(CVS)of the flow field.The effective filter width could be kept consistent with FDNS through adjusting the threshold value in order to compare the statistics of the flow field.It is found that the CVS can be effectively preserved by wavelet filtering.As to the particle statistical characteristics,the particle RDF seems to be better captured than the FDNS results due to the recovering of SGS structures.Meanwhile,it's obvious that the single-point particle statistics,such as the particle seen flow structural properties and the Lagrangian integration time scale are comparably less sensitive to the SGS structures than the particle pair dynamics statistics.So,in the filtering process based on the CVS,the relative errors of particle statistics above could be effectively reduced,which provides a new way for predicting the particle dynamics and also the construction of particle SGS model.Finally,based on the wavelet FDNS(WFDNS)flow field mentioned above,a structural SGS model based on differential filter(DF)is introduced to model the SGS velocity field seen by the particles.The results show that with the help of the structural SGS model,the multi-scale vortex structural information gets enhanced,and the prediction of particle diffusion and preferential concentration effects are improved.Through the comparison with the model validation in the FDNS field,the difference between the two cases is small as to the particle diffusion statistics,but the results of WFDNS+DF exhibit obvious advantages in the particle RDF and collision kernel.On the other hand,we also give out the particle statistics under different filtered fields with the Langevin pattern SGS model,it is found that the particle stochastic SGS model is aimed to compensate for the loss of turbulent kinetic energy in the sub-grid scales.Although it can effectively improve the accuracy in predicting particle diffusion statistic such as the kinetic energy and the Lagrangian integral timescale seen by the particles,but the stochastic model cannot be used to predict particle-pair dynamic statiscs.In general,the structural particle SGS model based on the extraction of coherent vortex structures shows great advantages in the modelling of various particle statistics,especially for the particle-pair statistics of small inertia particles.